Question

• Rectangle ABCD has a length represented by the expression (-2x+4) and a width represented by the expression (x+3). Rectangle EFGH has a length represented by the expression (5x-7) and a width represented by the expression (x - 1). Write an expression to represent the difference in the perimeters of Rectangle ABCD and Rectangle EFGH.

Answer 1

The perimeter of a rectangle of length L and width W is given by:

P = 2L + 2W

Rectangle ABCD has a length L = -2x+4 and a width W = x + 3

Compute the perimeter of this rectangle:

P(ABCD) = 2 (-2x+4) + 2 (x+3)

Note we used parentheses to separate both quantities from their factor 2. Now we apply the distributive property on both terms:

P(ABCD) = -4x + 8 + 2 x + 6

Joining like terms:

P(ABCD) = -2x + 14

Now for the rectangle EFGH which as a length L = 5x - 7 and a width W = x -1

Compute the perimeter of this rectangle:

P(EFGH) = 2 (5x - 7) + 2 (x - 1)

Joining like terms

P(EFGH) = 10x - 14 + 2x - 2 = 12x - 16

We are required to write an expression to represent the difference in both perimeters, that is:

Difference = P(ABCD) - P(EFGH)

Replacing the expressions obtained for the perimeters, we have:

Difference = -2x + 14 - (12x - 16)

Note we used parenthesed for the second perimeter since it's subtracting and the expression will alter its signs like shown below:

Difference = -2x + 14 - 12x + 16

Joining terms

Difference = -14x + 30